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Quantum theory is incredibly successful at describing our physical world and its limitations, at least at a small scale, yet many fundamental questions about the theory remain open. These range from fundamental questions like ‘where will quantum mechanics break down (if at all)?’ to practical questions like ‘what does it take to build a quantum processor that can outperform a classical computer?’ I study these types of questions using various mathematical tools that generally fall within the context of quantum information theory.

I am particularly interested in studying the limitations of quantum mechanics under realistic constraints such as relativistic causality or the limitations of a particular experimental setup. Although my work is theoretical, I enjoy collaborating with experimentalists and I am currently a member of two experimental quantum optics groups at the University of Toronto.

Non-local quantum operations

Quantum systems and quantum operations are more then just a sum of their parts. In many cases, global properties of composite systems cannot be broken down to properties of the individual subsystems. Moreover, global dynamics cannot be reduced to a series of local processes. Non-local objects (states, observables, dynamical processes etc.) play a central role in quantum theory. They include fundamental observables (e.g momentum), entangled ground states of Hamiltonians, measurement procedures, and the building blocks of many quantum information processing tasks. Understanding the limitations and advantages that arise from non-locality is therefore fundamental to the study of many physical phenomena. Moreover, many of the limitations related to non-locality are analogous to limitations in purely local scenarios (e.g the inability of photons to interact) so many results from the study of non-local operations have direct experimental applications.

The finite speed of light, and consequently the finite speed for information transfer imposes one major constraint for non-local dynamics. This constraint is usually framed in terms of time or communication resources i.e a dynamical process cannot be implemented faster than the time required to send information across some relevant space. Heisenberg’s uncertainty relations impose a second constraint. Roughly speaking, some non-local (global) operations require ignorance about the local dynamics. Entanglement can be used to preserve ignorance and overcome this constraint. In principle, given infinite entanglement and communication resources, it is possible to use quantum teleportation and make any non-local process a local process. But what happens when these resources are limited?

Instantaneous non-local operations

Instantaneous non-local operations are those that can be generated without communication resources. A particularly interesting subset of these are instantaneous non-local measurements. In the early days of quantum theory Landau and Peierls noted that some non-local (projective) measurements can violate causality. Fifty years later, Aharonov and Albert showed that some non-local measurements do not violate causality, and provided a scheme for measuring some non-local observables by using entangled ancilla systems. However, the Aharonov and Albert scheme works only for a small class of non-local observables, and only at the limit of a strong projective measurement. In general, it is still unknown which operations can and cannot be implemented instantaneously. Most non-local operations need to be examined on a case by case basis. If an operations can violate causality, we can conclude that it is impossible; if we can find an explicit scheme for performing it, we can conclude that it is possible. We can also try to circumvent causality by making the operation non-deterministic.

The study of non-local operations allows us to have a conceptual understanding of which operations are forbidden in quantum mechanics, or at least give us lower bounds on the time required to perform them. But the implications go beyond the study of locality and time, for example: the limitation that photons cannot interact is (mathematically) the same as the constraint on locality, so non-local measurement schemes can be converted into schemes for making measurements on photonic systems.

Related publications

A scheme for performing strong and weak sequential measurements of non-commuting observables, A Brodutch and E Cohen, Quant. Stud. (2016)

Quantum correlations

One of the interesting discoveries that came out of quantum information theory was the existence of quantum operations that require entanglement even though they are seemingly composed of purely local pieces. If these operations are a necessary piece of some physical system (e.g a quantum heat engine) then non-local resources (e.g entanglement) offer an obvious advantage over purely local ones. When this advantage is quantified, it can be used as a measure of quantum correlations.

Work on quantum correlations can be roughly divided into the mathematical side, e.g `what types of functions quantify quantum (or classical) correlations?’; the physical side e.g. `how can we use quantum correlations to quantify the advantage of non-local operations in a particular physical scenario?’ or `what is the role of quantum correlations in open system dynamics?’; and the quantum information side e.g. `what is the role of quantum correlations in quantum information protocols?’. By digging into these questions we learn about some fundamental aspects in quantum mechanics, particularly non-locality and the quantum-classical transition. We also discover new quantum protocols that can exploit the advantages offered by the more subtle aspects of non-locality.

Related publications

Why should we care about quantum discord? A Brodutch and DR Terno, In `Lectures on General Quantum Correlations and their Applications’ (2017)

Entanglement and deterministic quantum computing with one qubit,M Boyer, A Brodutch and T Mor Phys. Rev. A (2017)

Quantum operations on a curved background

Gravity may influence the way we treat information flow between two observers at different space-time points. In the relativistic setting, different degrees of freedom get mixed and the transformations of a system traveling from point A to point B depend on the precise trajectory between these points. Consequently there are no `standard’ reference frames that can be used to align the relevant physical apparatus.

Photons are possibly the simplest physical systems in terms of relativistic transformations since they can be treated classically to a very good approximation, i.e when gravity is sufficiently weak, we only need to account for the transformations of a classical electromagnetic wave. Photons are also the most interesting system from an experimental point of view since it is relatively easy to transmit photons from one gravitational potential to another. Consequently we can now try to design the types of experiments that would measure these gravitational effects on photons. Although the effects are small, the current trend towards putting quantum satellites in space makes these types of experiments reasonable in the not too distant future.

Semi-quantum computing

Quantum computers offer amazing technological promise and an extreme test of fundamental physics. The potential capabilities of universal quantum computers are driving researchers to push the boundaries of experimental and theoretical work in physics and computer science. However, despite immense progress, we are still far from building universal quantum machines. Semi-quantum computers are quantum information processing devices with fewer requirements (and fewer capabilities) than universal quantum computers, they offer possible avenues towards near future implementations and new theoretical insight into the boundary between quantum and classical physics.

A semi-quantum computing model can be defined in a number of ways, for example by taking a universal quantum computing model and removing some elements (often those that seem hard to implement). For each such model we may ask a number of interesting questions

1. What problems can it solve, and are those problems hard for a classical computer?

2. Is it indeed easier to implement than a universal quantum computer?

3. What are the conceptual properties that make it faster than a classical computer?

Finding the answer to the first two questions is one of the most important steps towards the near future implementation of quantum information processing devices. Answering the last question give us insight into the difference between our classical experience and the underlying quantum world.

Quantum foundations and weak measurements

Quantum mechanics is an incredibly successful physical theory that has remained virtually unchanged after almost 100 years of experimental and theoretical developments. Nevertheless, the theory has some drawbacks such as the so called `measurement problem’ and the lack of an intuitive description that does not involve a Hilbert space. These problems are often viewed as hints that the theory is an approximation of a more fundamental theory, but it is unclear what such a theory should look like.

One relatively new approach to this problem is via weak measurements, weak values and the time symmetric formalism. Weak values can be seen as fundamental physical quantities in a time-symmetric approach to quantum mechanics. They cannot be observed directly, but they can be observed after many repetitions of an experiment involving a weak measurement, i.e a measurement that has negligible back-action. Since the theory leading to weak values is grounded in standard quantum mechanics, all predictions are compatible with those of the standard theory, this also means that it encounters the same problematic issues. On the other hand, it does offer a different pot of view which has led to new insight and predictions that might have been missed otherwise. The ultimate goal of this research program is to find some hints of what we should look for in a theory that goes beyond quantum mechanics.